Stagnation Pressure of Imploding Hollow Shells

Movie: Self-similar solution of a spherically imploding shell in
a radius-time diagram. The inner shell surface and the trajectory
of the reflected shock are represented by thick lines. Fluid elements move
on dotted trajectories with almost constant velocities. The movie shows
the evolution of the density profiles with time. The fluid element
at r=r0 and t=t 0 is considered as an outer boundary.

Our motivation for employing this model is that the shell compression
at the time of stagnation (t=0) in realistic capsule implosions -- as
they would typically occur in inertial confinement fusion capsules -- can
be modeled surprisingly accurate by the self-similar description. This
leads to a scaling law for the ignition energy of ICF capsules which
corresponds quite well to numerical simulations of capsule implosions.